








2.
Outcome: Probability: 0 ? 1 .1 2 .2 3 .5
a) What value should replace the question mark if this is
a probability distribution?
b) Is this a discrete or continuous distribution?
Explain.
c) What is the mean of this probability distribution?
d) What is the standard deviation of this probability
distribution?
3. John has tossed a coin five times and has had this sequence of results: Heads, Heads, Tails, Heads, Tails. He is wondering how likely this result is compared to the sequence: Heads, Heads, Heads, Heads, Heads. What is the right answer?
4. A game of chance is played by spinning a wheel and paying the amount that comes up. There are four possible outcomes:
x p(x) $1 .50 $2 .30 $5 .15 $10 ??
5a) Show that P(x) = x/11  .25 for x = 4, 5, 6, 7 is a probability distribution.
6. Jack has a trick coin that will come up heads twothirds of the time.
7. Here is an example of a discrete, uniform probability distribution:
x p(x) 0 .2 1 .2 2 .2 3 .2 4 .2
Find:
What is the expected value of x?
What is the standard deviation of this distribution?
8. The game show Deal or No Deal features 26 suitcases with various amounts of money. The contestant chooses one than then begins to open the others. At the end of each round, the "Banker" makes an offer to end the game. The game ends either when the player takes the offer, or when he or she has opened all 25 suitcases that he or she did not choose, in which case he or she gets the amount in the chosen suitcase.
9. P(x) = .5 x/10 is a probability distribution for x = 1, 2, 3, 4.